There's the problem. Batman shouldn't be in the same universe any more than Jonah Hex should. In a world with those other heroes, Batman isn't needed. Because he is ineffectual compared to them.
I think I've heard enough Batfans claim Batman can "defeat" (there...that better?

) every single hero in the universe to know they require more than Batman being "integral/important to the team" or "hold his own". They need him to be the supreme hero that can wipe everyone else out if he wants to. He's too popular to be a sidekick....so the writers have to go to work and make him unbeatable....while any other hero he fights will turn into a moron.
http://judgescourt.deviantart.com/art/Superman-vs-Batman-39965852
The interesting thing about Batman fans is how they claim to dislike Superman because he's invincible and how much they favor "realism". ...But then with their next breath they'll claim Batman can defeat Superman.
That's the main reason Batman should exist in his own universe (with maybe Green Arrow, Hawkman, Black Canary, and other lesser heroes). He's logic based and the others aren't.
In the universe he does exist in, he is the
least realistic of all super heroes. The type of villains that run around in
OUR world would take out a Batman in about two weeks. So as unrealistic as he is in our universe....amp that up by 100 in the DC universe. If any of the super villains did buy into this idea that Batman is the supreme being on the planet...Bats is going bye bye.
(I would just trick the Flash into believing it and that Batman was coming to kill him. Batman would be eating his breakfast one second and sinking to the bottom of the Pacific Ocean bound head to toe with duct tape...naked... one second later. "Plan" your way out of that one!
)
That's why the JLA comic is so silly compared to the Batman comic to me. The Avengers has a similar problem with Capt America...but at least they don't have to pretend Cap can defeat every hero on the planet. So I can buy that Cap would be useful for his leadership skills. Lord help the Capt America character if he ever becomes their most popular hero at some point. Suddenly we would have Cap defeating the Hulk and Thor. Popularity can be a curse.